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Given the function ƒ(x) = 5x¹ + 75x³ + 315x² + 405x, and one of its factors is (x + 9), write f(x) as a product of linear factors with integers. f(x) =

Given the function ƒ(x) = 5x¹ + 75x³ + 315x² + 405x, and one of its factors is (x + 9), write f(x) as a product of linear factors with integers. f(x) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given the function f(x) = 5x¹ + 75x³ + 315x² + 405x, and one of its factors is (x + 9), write f(x) as a product of linear factors with integers. f(x) =
Transcribed Image Text:Given the function f(x) = 5x¹ + 75x³ + 315x² + 405x, and one of its factors is (x + 9), write f(x) as a product of linear factors with integers. f(x) =
Expert Solution
Step 1

Giv

    fx=5x4+75x3+315x2+405x

   One of its factors is x+9

Factor out common terms:

        =5xx3+15x2+63x+81

  The polynomial x3+15x2+63x+81 can be factorized by using the rational root test.

  To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=-3

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